Physics Lab #4
Projectile Motion
Theory
For an object falling with no horizontal motion in earth's gravity in such a away that we can ignore air resistance, its motion up and down is described by y = voyt -1/2 gt2, where y is the position relative to the starting position, vo is the starting velocity, t is the time and g is the acceleration due to gravity (g = 9.8 m/s2). Up is considered the positive direction for this equation. This equation is also valid for describing the up and down (vertical) motion of an object traveling in a parabolic arc. The back and forth (horizontal) motion is much simpler because there is no accleration horizontally, so the velocity (vox) is constant and x = voxt describes the horzontal position, x.
From trigonometry we can figure out how tall something is, call it h, if we know how far we are from the base
of the object, call it d, and we measure the angle, A, from the base to the top of the object. We get:
h = d tan(A)
Procedure
We will use the funnelator (a giant slingshot) to shoot a rubber ball upward. We will use trigonometry to figure out the height of the ball at maximum and then time the duration of the fall until it hits the ground. We will do a number of launches. You should work in groups of three. One group member will join the launch group. One will be the "sighter" and the last will be the "timer and angle measurer". Remember reading errors.
- We will measure out a distance of 30m from the launch site to the measuring site. (Note this distance with error.) I will show the lanuchers what to do.
- When the ball is launched one partner should sight along a meter stick and hold the stick in place where the maximum height occurs. At this point the timer should start the stop watch and stop it when the ball hits ground. Then measure the angle the meter stick makes with the ground. Your data table will have: distance to base, angle and time.
- We will do some angled launches to get a view of a parabolic trajectory. You simply need to make sketches of the shape of the trajectory.
Calculations
At the peak of the ball's path it has zero velocity so our equation simplifies as in the second lab. (Write the equation for the height as a function of time using the first equation in the theory section.) The distance it travels down, h, in the time measured is given by the trig equation in the theory section. (To be more exact you should add the height from the ground to eye level. Why?) Derive the equation for the relationship between the angle and the time by using these two equations. (It will also include g and the distance to the launch station.) I will show you how to use your data to get a graph that allows you to "measure" g. You will compare the measured g to the known one.